1) The darkness is the power you utilize, sourced from the "Abyss". Rather than a location, it's more implied to just be the darkness within ones soul. It is not an evil force, but it is volatile and emotional inherently, which makes it dangerous to harness.
2) The darkside in the MSQ appears in two incarnations, the first a form of frustration that everyone coens to you with their problems, and later, a manifestation of the WoL's pain and a desire to escape it. The most important thing to note is that these are desires are not external-- the WoL really does feel these things, and these supresses emotions are manifesting as a Darkside. In both cases, the darkside is not a bad thing, but if not accepted by the dark knight, they will overtake you. In the lorebook, it is stated that those who lose control in such a way literally combust in stygian, abyssal flame.
In short, the darkside can overtake the person to commit heinous acts, yes, but some part of the person must want that.
3) The soulstone isnt strictly required to use the dark magics in lore. But if you dont have a healthy approach to dealing with your power it will probably hurt you or corrupt you!
4) No. A soulstone, contrary to its name, doesnt absorb souls. A soulstone is exposed to the experience and memory of its user over their profession, engraining memory, instinct and experience into the tiny grooves of the crystal. Soul stones can act differently depending on class-- in the dark knights case, touching the soulstone allowed the darkness within the WoL to manifest as a Darkside, which introduces itself as Frey (the name of the previous owner) but who later names itself Esteem. Frey isnt literally there, it's just using the name of the dead dark knight to further its goals.
5) the "fuel" of the dark knight is not entirely spelled out. While negative and passionate emotions seem a basic one, the darkside seems to embody the emotional states that the wielder others within themselves-- in the WoLs case, their irritation and frustration with the world, and their own grief. As stated previously, a dark knight is only stable when they confront these raging feelings and accept them. This doesnt mean they go away, just that they do not ignore or allow them to rule them. Of someone is using their rage to fuel their power, and that rage is eroding them as a person, I dont think that dark knight will last very long.